Trump supporters found themselves more strongly associated with such stories than the Democrats (not surprising given his support among right-wing social media,) so they attempted to reframe "fake news" as, itself, a fake phenomenon invented by the left to discredit alternative media out of fear of the threat it presented to the leftist media establishment status quo.
This to further the narrative that the mainstream media was little more than a propaganda wing of the DNC and its globalist masters, and that any Trump-critical stories from the MSM were likely to be fabrications and thus not to be trusted (but you could trust those stories on your Facebook feed about HRC having Parkinsons' disease or running a child sex slave ring out of a pizza parlor.)
And then Trump himself picked up on it somehow and now likes to label anything and anyone that criticizes him as fake news.
Ironically, the least likely thing to be called fake news nowadays is news that is actually fake.
If FOX news runs front-page mugshots non stop every time an immigrant commits a crime, that shows a massive bias and leads its readership to an incorrect worldview, but it's not "fake". If Honest Truth Online runs a story that a missing girl was murdered by an immigrant based on miniscule to no evidence, that's fake news.
Fake News is propaganda that consists of deliberate disinformation or hoaxes. Nothing mentioned mention here falls into a category of Fake News. Fake News creates cognitive dissonance and distrust. More subtler methods work differently.
"But mainstream media also does Fake News" arguments are whataboutism.